








•J0> 



s 



QC 

91 

On 







LIBRARY OF CONGRESS. 

^ 

©pit. *•.... iiwWt *; 

UNITED STATES OP AMERICA. 



The 



Yard or the Metre, 



WHICH 



Will Ye Choose. 



DR, WATSON F. QUINBY. 



I 89 I . 



Wilmington, Del. 

W. COSTA, The Printer, 

811& Shipley St. 



Entered according to Act of Congress, in the year 1891, by Dr. Watson F. Quinbv. in the 
office of the Librarian of Congress, at Washington, D. C. 



The 



Yard or the Metre, 



WHICH 



Will Ye Choose. 



Dr. WATSON F. QUI N BY. 



I 89 I. 



Wilmington, Del. 

W. COSTA, The Printer, 

811% Shipley St. 



LC Control Number 



tmp96 027097 



THE METRIC SYSTEM. 



EXPRESSED IN INCHES. 



MEASURES OF LENGTH. 



INCH. 



Millimetre, 


- 


03937 


Centimetre, - 


- 


39371 


Decimetre, 


3 


93710 


Metre, 


39 


37100 


Decametre, 


- 393 


71000 


Hectometre, - 


3937 


1 0000 


Kilometre, 


- 39371 


00000 


Myriametre, - 


- 3937io 


00000 


MEASURES OF 


CAPACITY. 




CUB. IN. 


Millilitre, 


.061028 


Centilitre, 


.6I0280 


Decilitre, 


6.I02800 


Litre, 


6l.028000 


Decalitre, 


6I0.280000 


Hectolitre, 


6I02.800000 


Kilolitre, 


- 6I028.000000 


Myrialitre, 


6I0280.000000 


MEASURES OF 


WEIGHT. 




GRS. 


Milligramme, 


.0154 


Centigramme, 


- -1543 


Decigramme, 


1-5434 


Gramme, 


I5.4340 


Decagramme, 


154.3402 


Hectogramme, 


1543.4023 


Kilogramme, 


- 15434-0234 


M3'riagramme, 


154340. 


2344 



THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 



FIG. I. 

. OOOOOOOOOOOOOO I 
. OOOOOOOOOOOOO I 

•OOOOOOOOOOOO I 

.OOOOOOOOOOOI 
.OOOOOOOOOOI 
.OOOOOOOOOI 
. 00000000 1 
.OOOOOOOI 
.OOOOOOI 
. 00000 1 
.OOOOI 
.0001 
.001 
.01 
. I 
I. 
10. 
IOO. 
IOOO. 
I 0000. 
I 00000. 
I 000000. 
I 0000000. 
I 00000000. 
I 000000000. 
I 0000000000. 
I 00000000000. 

I OOOOOOOOOOOO. 

I OOOOOOOOOOOOO. 
I OOOOOOOOOOOOC K i . 

I OOOOOOOOOOOOOOO. 



THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 5 

Fig. i is the numeration table. It has no reference to any- 
thing in particular, only number. 

The dots are decimal points. All numbers on the left hand 
side of the decimal points are whole numbers. 

All numbers on the right hand side of the decimal points are 
fractions. 

Units, tens, hundreds, thousands, tens of thousands, hundreds 
of thousands; millions, tens of millions, hundreds of millions; 
billions, tens of billions, hundreds of billions ; trillions, tens of 
trillions, hundreds of trillions ; quadrillions. 

I have stopped at quadrillions, but that is but a small portion 
of the numeration table. 

You may go on to quintillions, sextillions, octillions, 
decillions, dodecillions, clean on up to centillions if you want to ; 
more than you can count in a life time. 

The decimalization of this table is perfect ; its extent 
practically unlimited, both upward and downward, and its nomen- 
clature has been skillfully devised. 

Now, our system of weights and measures has been joined 
to this numeration table, and they therefore partake of all its 
excellencies. 

You may call the unit any measure or weight, and then 
decimalize it, either upwards or downwards to any extent desired. 
An inch; tenth of an inch, hundredth of an inch, thousandth of 
an inch. Or a yard, or a mile ; ten miles, hundred miles, thous- 
and miles. Or a cubic inch, tenth of a cubic inch, hundredth of 
a cubic inch. Or an ounce, ten ounces, hundred ounces, thousand 
ounces. 

FIG. 2. 

.001 Millimetre 
.01 Centimetre 
. 1 Decimetre 
1 . Metre 
Decametre 10. 

Hectometre ioo. 
Kilometre iooo. 
Myriametre, ioooo. 



6 THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 

Now Fig. 2 is the metric system ; what there is of it. Deci, 
centi, milli and that is all ; tens, hundreds, thousands, and there 
it stops. 

If you wish to go further, you come to subfractions. Deci, 
centi, milli, are no better than tens, hundreds, thousands, and 
not as good for English ears. 

And you are asked to exchange our splendid numeration 
table for this miserable abortion. For the Metric System is 
simply an abortive attempt to create a numeration table, and 
failed dismally. Be not deceived because it takes three tables to 
do what one would do. 

Fig. 3 shows the Metric System applied to the inch, cubic 
inch and grain. Inch, deci inch, centi inch, milli inch. 

fig. 3. 



.001 


.001 


.OOI 


.01 


.01 


.OI 


.1 


.1 


.1 


1. inch r. cub. 


inch 1. grain 


10. 


10. 


10. 


100. 


100. 


IOO. 


1000. 


1000. 


1000. 


1 0000. 


1 0000. 

FIG. 4 


I OOOO. 


.001 


.OOI 


.001 


.01 


.OI 


.01 


.1 


.1 


.1 


1. metre 1. litre 1. gramme 


10. 


IO. 


10. 


100. 


IOO. 


IOO. 


1000. 


IOOO. 


IOOO. 


toooo. 


I OOOO. 


I OOOO. 



Now, it is evident that one table would do for all of these. 
Fig. 4 gives the metre, the litre and the gramme. It is 
equally plain that one table would answer for all of these. 

1 1 is a defect to attach any particular value to the numeration 



table ; for then one table is good for the metre only 



one is good 



THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 



for the litre only ; and one for the gramme. But ours is good 
for all and every measure or weight ; for the inch, the yard or the 
ounce ; or for the metre, the litre or the gramme. 

It is also of unlimited extent both upward and downward ; 
whereas the metric is only tens, hundreds, thousands. 

The cubic tenth of an inch is contained in the cubic inch 
one thousand times. 

The cubic hundredth of an inch is contained in the cubic 
inch one million of times. 

The cubic thousandth of an inch is contained in the cubic 
inch one billion of times. 

The cubic ten thousandth of an inch is contained in the 
cubic inch a trillion of times. 

The cubic hundred thousandth of an inch is contained in the 
cubic inch a quadrillion of times. And so on you may go down 
to the very infinitesimals of matter, and find it all decimal, all 
cubic and all in entire harmony with the numeration table. 

Now what has the metric system to offer for all this ? Why, 
nothing. 

But it is claimed, that by means of the prefixes, that as soon 
as a number is pronounced, you know on which side of the 
decimal point it is. The Latin prefixes show that the number is 
on the right hand side of the decimal point. The Greek pre- 
fixes show that the number is on the left hand side of the decimal 
point. 

That is true as far as it goes ; tens, hundreds, thousands. 
But we have no need of these prefixes. For we arrive at the 
same result by means of the termination of the word. 

Every verb in the English language has two forms. He 
says, he saith ; he goes, he goeth ; he does, he doeth ; and so on, 

Advantage has been taken of this in constructing our table 
to accomplish the same object by the suffix, as the metric system 
does with its prefixes. So that you know as soon as a number is 
pronounced, on which side of the decimal point it is. 

If it ends in th, it is on the right hand side, among the 
fractions. Any other termination places it on the left hand side 
among the whole numbers. 



THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 



NUMERATION TABLE. 



quadrillionth 

hundred trillionth 

ten trillionth 

trillionth 

hundred billionth 

ten billionth 

billionth 

hundred millionth 

ten millionth 

millionth 

hundred thousandth 

ten thousandth 

thousandth 

hundredth 

tenth 



. oooooooooooooo I 

. ooooooooooooo I 

. oooooooooooo I 

.00000000000 I 

.OOOOOOOOOOI 

.OOOOOOOOOI 

•OOOOOOOOI 

.OOOOOOOI 

.OOOOOOI 

.OOOOOI 

.OOOOI 

.0001 

.001 

.01 

.1 



1. unit 
10. tens 
100. hundreds 
1000. thousand 
1 0000. ten thousands 
100000. hundred thousands 
1000000. million 
10000000. ten millions 
1 00000000. hundred millions 
1 000000000. billion 
1 0000000000. ten billions 
1 00000000000. hundred billions 
1 oooooooooooo. trillions 
1 ooooooooooooo. ten trillions 
1 oooooooooooooo. hundred trillions 
1 000000000000000. quadrillion 



THK YARD OR THE MKTRK, WHICH WILL YE CHOOSE. 9 

Ten, tenth ; hundred, hundredth ; thousand, thousandth ; 
million, millionth ; so that with a single suffix, we attain the 
end which they might gain by any number of prefixes. 

But they have only three one way and four the other ; 
whereas we can go up or down to an unlimited extent. But we 
also have prefixes. After tens, hundreds, thousands, then comes 
the mil, the bil, the tril, the quadril, and so on to any extent 
desired, up to centil if you will. 

Our prefixes are the same upward and downward. So that 
our system is superior to the metric in this very matter, and we 
have no use for their prefixes. 



IO THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 



ANOTHER FORM OF THE NUMERATION TABLE. 
O 
O 
O 

o trillionth 

o hundred billionth 

o ten billionth 

o billionth 

o hundred millionth 

o ten millionth 

o millionth 

o hundred thousandth 

o ten thousandth 

o thousandth 

o hundredth 

.1 tenth 
i . unit 
o tens 
o hundreds 
o thousands 
o ten thousand 
o hundred thousand 
o million 
o ten millions 
o hundred millions 
o billion 
o ten billions 
o hundred billions 
o trillion 
o ten trillions 
o hundred trillions 
o quadrillions 



THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 



II 



THE METRIC SYSTEM. 



Thousandths, 

Hundredths, 

Tenths, 

Tens, 

Hundreds, - 
Thousands, 
Ten thousand, 



o milli 

o centi 

. i deci 

i . unit 

o deka 

o hecto 

o kilo 

o myria 



12 THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 

Again, the metric system claims to be the decimal system 
par excellence. You would naturally suppose then that its 
decimalization was perfect. I will show that it is not. They 
blundered at the very outset of their decimalization. 

The decimetre, the tenth of a metre, is on the wrong side of 
the decimal point. The metre is so near forty inches, that to 
illustrate, we will call it that, as shown in Fig. 5. 

fig. 5. fig. 6. 

Millimetre .04 .02 milli 

Centimetre .4 .2 centi 

Decimetre 4. 2. deci 

40. Metre 20. scruple 

400. 200. 

4000. 2000. 

Fig. 5 shows the decimetre on the left hand side of the 
decimal point among the whole numbers. 

Now, the centimetre, any one would call four tenths, and 
four tenths it is ; and the millimetre is four hundredths. Now, 
if you call the unit in Fig. 1 a metre, the decimetre is on the 
right side of the decimal point among the fractions, where it 
ought to be. So the decilitre is on the wrong side of the decimal 
point and the decigramme is on the wrong side of the decimal 
point ; and it is a blunder that cannot be corrected. 
Fig. 6 is also a good illustration of the same fact. 
I have thus shown that the metric system is exceedingly 
limited ; that it is useless to us, and that it is imperfect. One 
of the most singular things in this connection is, that Fig. 1 is 
the French numeration table, devised by their own wise and 
skillful mathematicians, and which we use in common with 
them, in preference to the English system of notation. 
We will now proceed to measures of length. 
The metre is composed of 39.37 inches. This sum is not 
evenly divisable by any whole number, which makes it exceed- 
ingly unhandy in practical work. 

The inch does not belong to the metre, but they were forced 

to adopt it, from its great practical usefulness. They might have 

made a metric inch that would have harmonized with the new 

measure, but that would have made greater difficulty in introduc- 

1 j other countries. 



THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 1 3 

Now, as an abstract number, any mathematician would say 
that 36 was a better number than 39.37. 

The number 36 will divide evenly into halves, quarters, 
thirds, sixths, ninths, twelfths and eighteenths ; and 24 inches 
into halves, thirds, quarters, sixths, eighths and twelfths ; and 
12 inches into halves, thirds, fourths and sixths and 6 inches 
into halves and thirds. 

But the yard of 36 inches is not only evenly divisable by 
even numbers, but b} 7 " all the uneven ones as well. In this way. 
There are 360 tenths of an inch in a } T ard ; 324 ninths; 288 
eighths ; 252 sevenths ; 216 sixths ; 180 fifths ; 144 fourths ; 108 
thirds; 72 halves; 396 elevenths, and 432 twelfths. 

In the two-foot rule, there are 288 twelfths; 264 elevenths ; 
240 tenths ; 216 ninths ; 192 eighths ; 168 sevenths ; 144 sixths; 
120 fifths ; 96 fourths; 72 thirds, and 48 halves. 

The foot rule will divide as follows : 144 twelfths ; 132 
elevenths of an inch; 120 tenths; 108 ninths; 96 eighths ; 84 
sevenths; 72 sixths; 60 fifths; 48 fourths; 36 thirds and 24 halves 
of an inch. 

This seemed to me a wonderful series of numbers ; so I set 
them down as follows : 



% 3 r ds 4ths 5ths 6ths 7ths 8ths gths ioths nths i2ths 

72. 108. 144. 180. 216. 252. 

48 72 96 120 144 168 

24 36 48 60 72 84 



288. 


324- 


360. 


396. 


432 


192 


216 


240 


264 


288 


96 


108 


120 


132 


144 



144 216 288 360 432 504 576 648 720 792 864 

And when that was done, I saw that I had before me a 
system of Logarithms ; but differing from Napier's in that the 
numbers under the indices were not geometrical series, but the 
product of the indices with a common multiplier. In the upper 
line the multiplier was 36. In the next line it was 24. In the 
third line it was 12. In the fourth line it was the sum of all of 
these which is 72. 



14 THE YARD OR THE METRE, WHICH WIEE YE CHOOSE. 



o o 



8 to 



to 



Go 









o 






Go 

p 


Co 




o 
o 

p 


-p^ 




o 


-£> 


►3 






% 




w 







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3 


o 
o 
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Cn 




Cn 


Cn 


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p 




# 







3* 






oT 


p 


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M 

o 
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On 




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o 







oo qo O 

o °° o 



o 
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o 
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8 o - 8 

O 00 

o 
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THE YARD OR THE METRE, WHICH WILL, YE CHOOSE. 



15 



LOGARITHMIC TABLE- 



OO, 
IO. 
2 ! 0, 
30. 
40. 
5,0. 
60. 

7 0. 

80. 

90, 

IO I. 



II 
12 
13 
14 
15 
16 

17 
18 

J 9 
20 
21 



00000 
1 0000 
20000 
30000 
40000 
50000 
60000 
70000 
80000 
90000 
00000 
1 0000 
20000 
30000 
40000 
50000 
60000 
70000 
80000 
90000 
00000 
1 0000 



16 THE YARD OR THE METRE, WHICH WILX YE CHOOSE. 

Here are the two systems compared. 

In Napier's the numbers under the indices are increased 
by multiplying by 10 each time. 

In the other the numbers are increased by adding 10 each 
time. 

Any other number besides 10 may be used in either case. 

In Napier's system, multiplication and division are accom- 
plished. 

In the other, addition and subtraction are accomplished. 

A name seems to be wanting for the numbers under the 
indices. I propose ondices. 

Then, in Napier's plan the sum of any two indices will 
be the indice of the product of the two ondices ; and the dif- 
ference of any two indices will give the indice of the quotient of 
their two ondices. 

In the new S3^stem, the sum of any two indices will give the 
indice of the sum of their two ondices ; and the difference of 
any two indices will give the indice of the difference of their two 
ondices. 

Still another logarithmic series may be formed, and based on 
the relation of the cubic inch to its decimal fractions. 



THE YARD OR THE METRE, WHICH WILE YE CHOOSE. I J 



IO 



IOOO 



IOO 



I OOOOOO 



IOOO 



IOOOOOOOOO 



IOOOO 



IOOOOOOOOOOOO 



I OOOOO 



I ooooooooooooooo 



I OOOOOO 



I ooooooooooooooooo 



1 8 THE YARD OR THE METRE, WHICH WILE YE CHOOSE. 

The multiplication of the indices gives the indice of the 
product of their ondices. The division of the indices gives the 
indice of the quotient of their ondices. 

If all of the fractional divisions of the inch were marked 
upon any one of our rulers, the rule would contain the elements 
of logarithms. 

You ma} 7 make almost an}' division of the inch, as thirteenth, 
fourteenth, fifteenth, sixteenth, eighteenth, thirty-second, sixty- 
fourth, or hundreds, or thousands, and when multiplied by 36 
the resulting numbers will be remarkable for their even sub- 
divisions. 

All this is very convenient for practical work. 

Now, the number of inches into which the metre has been 
divided will not permit of any of this even and convenient sub- 
division. The metre consists of thirty-nine inches and three 
hundred and seventy-one thousandths of an inch ; the decimetre 
is three inches and nine thousand three hundred and seventy-one 
ten thousandths of an inch ; the centimeter is thirty-nine thous- 
and three hundred and seventy-one hundred thousandths of an 
inch ; and the millimetre is three thousand nine hundred and 
thirty-seven hundred thousandths of an inch. The litre consists 
of sixty-one cubic inches, and twenty-eight thousandths of a 
cubic inch. The gramme is equal to fifteen grains and four 
hundred and thirty-four thousandths of a grain. 

It is evident that the inch and the metre were not made for 
each other. Yet is the metre expressed in inches and fractions 
of an inch. And the yard is also expressed in inches. Hence 
it follows that neither the yard nor the metre is the real unit of 
length, but the inch. 

As to how many inches you will have in your measuring 
rule then, is a matter of practical convenience. Measured by 
that standard, the yard and its subdivisions have much the 
preference over the metre. 

For as I have shown, the yard can be divided evenly and 
without remainder by all numbers. Whereas, the metre expressed 
in inches is not evenly divisable without fraction, by any number. 



THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 1 9 

In our tables the word ounce is used to denote volume and 
weight. 

But there is an implied lineal ounce of twelve tenths of an 
inch in length, which could be made useful in decimalizing our 
measures of length. 

Ten linear ounces make one foot, twenty make two feet, 
thirty make one yard ; one hundred ounces make ten feet and a 
thousand ounces make one hundred feet, and so on ; and ten 
ounces cubed make a cubic foot. This foot can be decimalized 
downward and upward the same as the cubic inch. The one foot 
rule connects our measures of length with those of volume. 

The cubic foot may be considered the standard of weight 
and volume ; as it weighs one thousand ounces avoirdupois of 
water. It will weigh 62^ pounds Avoirdupois ; or 60 Troy, or 
60 Apothecary pounds. 

Our system of mensuration is then substantially perfect. 
But it is claimed that the metre is commensurable with the 
earth ; that it is definitely the one ten millionth of a quadrant of 
the meridian passing through Dunkerke, France. 

Meridian circles are great circles around the earth, passing 
through both poles. A quadrant of a meridian then extends 
from the pole to the equator. 

Now, the French never measured a quadrant of the meridian. 
They have never been to the North pole ; if they did, they 
could not measure across the ocean. No; they measured an arc 
of a meridian extending from Dunkerke to Barcelona, and the 
rest is too much guess work. 

More recent measurements tend to invalidate the accuracy of 
the French measure ; and Sir John Hershel asserts that the 
English yard is more nearly an aliquot part of the earth's axis, 
than the metre is of the quadrant of the meridian ; and it is 
therefore more nearly earth commensurable. Besides, there is 
but one axis, which is also a straight line passing through the 
earth from pole to pole ; whereas, there are thousands of meridian 
lines, all of unknown curve, and no two could measure alike. 

We now come to measures of volume and of weight. 

The unit of volume is defined to be "a small cube whose 
dimensions are known." The unit must be a cube. The unit 



20 THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 

of volume for what are called English weights and measures, is 
the cubic tenth of an inch. It is not so set down in the books, 
but it is the fact, nevertheless. 

It might be called the central unit, for you can go from it 
both upward and downward to an unlimited extent. 

The cubic tenth of an inch is contained in the cubic inch 
one thousand times. The cubic hundredth of an inch, one 
million times. The cubic thousandth of an inch, a billion of 
times ; the cubic ten thousandth of an inch, a trillion of times ; 
the cubic hundred thousandth of an inch, a quadrillion of times, 
and the cubic millionth of an inch is contained in the cubic inch 
a quintillion of times ; and so on you may go down to the very 
atoms of matter, and find it all decimal, all cubic and all in strict 
conformity to the numeration table. 

In these days, when more and more account is taken of small 
things, this part of the English tables might prove of consider- 
able utility, especially among chemists. 

A cubic inch contains iooo units. 

Tenths iooo units . i 3 

iooo 
Hundredths ioooooo Monas .oi 3 

iooo 



Thousandths iooooooooo Minas .ooi 3 

iooo 



Ten Thousandths ioooooooooooo Motes .oooi 3 

iooo 
Hundred Thousandths iooooooooooooooo Mites .ooooi 3 

iooo 
Millionths i oooooooooooooooooo Atoms .oooooi 3 

The cubic tenth of an inch which I will henceforth call the 
unit, is the one thousandth part-of a cubic inch. It is therefore 
expressed as .001. The grain consists of four of these units of 
water, and so is expressed as .004. That is not so set down in 
the books cither. 

The modern avoirdupois grain is .00396 plus of a cubic inch. 
But that is evidently out of order in a cubic system. How much 



THE YARD OR THE METRE, WHICH WIEE YE CHOOSE. 



21 



is it out of order ? It is out of order by the 400000th of a cubic 
inch. 

.00396 
.00004 



.004 



That is a very small matter ; yet it is like the sharp point of 
a railroad switch, which can turn yon rushing train off the main 
track and side track it. 



Fig. 7. 



a 



1 i 1 



Fig. 7 represents a cubic inch, with its base divided into 
tenths ; a is the unit of volume. 

There are 250 of these .004 grains in a cubic inch of water. 

The tables give 252^ grains in a cubic inch, but that is 
because the grains have become too small in the wear and tear of 
the centuries. 



22 THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 

Here is a grain reduced to atoms. 




4000000 

1000 
4000000000 Motes 

1000 
4000000000000 Mites 

1000 
4000000000000000 Atoms 

The thousandth part of a grain is 4 monas. The millionth 
of a grain is 4 minas. The billionth of a grain is 4 motes. The 
trillionth of a grain is 4 mites ; and the quadrillionth of a grain 
is 4 atoms. 

Cubic in. 
61.028 Litre 
1000 



61028.000 units of Yolume 
1000 



61028000 Monas 

1000 
61028000000 Minas 
1000 



61028000000000 Motes 

1000 
61028000000000000 Mites 

The thousandth part of a litre is 61 units and 28 monas. 
The millionth of a litre is 61 monas and 28 minas. The bil- 
lionth of a litre is 61 minas and 28 motes, and so on. Or, the 
thousandth part of a litre may be expressed as 61028 monas. 
The millionth of a litre then is 61028 minas, and so on. 



THE YARD OR THE METRE, WHICH WILE YE CHOOSE. 



23 



The litre itself 61028 units. So the thousandth part of a 
millilitre is 61028 minas. 

I cannot do anything with the gramme without correcting 
the grain. The litre is=6io28 units. The gramme is one thous- 
andth part of this 61.028 units=i5.257 grains. 

Gramme. 

J 5- 2 57 S rs - °f - 00 4 cu b- in. 
4 

units 



61.028 

1000 



61028.000 
1000 



Monas 



61028000 Minas 

1000 
'61028000000 Motes 

The thousandth part of a gramme is 61028 minas. The 
millionth of a gramme is 61028 motes, and so on. So this grain 
of 4 units makes the litre harmonize with the gramme. 

There are none of our measures of volume that are evenly 
commensurable with the cubic inch, except the cubic foot ; and 
that is not in use as a measure. Nor is the litre any better off, 
there being a long string of decimals. 

But when it comes to measures of volume, our system drops 
the cubic inch and takes the cubic ounce. 

Fig. 8. 
d 



a 



c 
b 



24 THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 

Ill Fig. 8 d represents the cubic ounce, c the cubic inch, b 
the cubic drachm, and a the unit of volume. The base of the 
figure is divided into tenths of an inch. The unit of volume is 
one tenth cubed ; the drachm is six tenths cubed ; the inch is 
ten tenths cubed ; the ounce is twelve tenths cubed. 

The grain contains 4 units; the drachm 216 units; the 
inch 1000 units, and the ounce 1728 units. The drachm contains 
54 grains ; the inch 250 grains, and the ounce 432 grains. This 
is the avoirdupois or cubic system I am on now. It is entirely 
cubic throughout. 

The modern ounce is 437^2 grains, which is 5^ grains too 
much, which is owing to the grain having become too small. 

The ounce of 432 grains is the old commercial ounce, which 
has descended from the Greeks to the Romans, and from the 
Romans to us. 

The cubic foot contains 1728 cubic inches and 1000 of these 
ounces. 

As to the ounce, the cubic foot is decimal ; as to the inch it 
is duodecimal. 

This ounce is an exact epitome of the cubic foot ; the tenth 
of an inch is one corresponding to the inch of the other. 

Or Fig. 7 may represent the cubic foot, and a the cubic 
ounce. 

As a standard of volume, the cubic foot is unique. 

It contains 1728000 units; 432000 grains; 8000 drachms; 
1728 cubic inches and 1000 ounces. 

The avoirdupois ounce contains 1.72S cubic inches. It is 
usually set down as 1.732 cub. in., but that is one grain too 
much and requires an ounce of 433 grains. 

This last ounce agrees with one old system of weights and 
measures, but they were not cubic. 



THE YARD OR THE METRE, WHICH WILE YE CHOOSE. 



25 



8 


= 


16 


= 


32 


' = " 


64 < 


= 


128 


== 


256 


= 


512 


= " 


1024 


= 



The avoirdupois measures are as follows : 

4 ounces=one gill . 

half pint. 

pint. 

quart. 

half gallon. 

gallon. 

peck. 

half bushel. 

bushel. 

There are no fractions or decimals here. 

The gill is half a cube. 

The half pint is a perfect cube. 

The pint is a double cube. 

The quart is half a cube. 

The half gallon is a cube. 

The gallon is a double cube. 

The peck is half a cube. 

The half bushel is a cube. 

The bushel is a double cube. 

Even the grain is half a cube. 

The avoirdupois is a system of one weight and two measures. 

There is a liquid measure and a dry measure, which are to 
each other in volume as 4 is to 5. 

This difference is founded on the nature of the substances to 
be measured ; as for instance, water and wheat. 

Sixteen ounces make a pint, and 16 ounces make a pound. 
'"A pint of water (then) is a pound of water." 

If a pound of water is=27,648 cubic in., a pound of wheat 
is=34.56 cubic in. This implies that as there is a wet grain of 
.004 cubic in., there is a dry grain of .005 cubic in. A wet pint 
-contains as many wet grains as the dry pint does of dry grains. 



Dry 

Cub. in. 



Wet 
Cub. in. 



Grs. 



One gill === 8.64== 6.912= 1728 

" pint = 34.56= 27.648= 6912 

" quart == 69.12= 55.296=13824 

"" gallon =276.48=221.184=55296 



Po. 


Ou. 


Drams. 


Grs. 


I 


16 


128 


6912 




i 


8 


432 






1 


54 
1 



26 THE YARD OR THE METRE, WHICH WILE YE CHOOSE. 

The same is true of the ounces; but the dry ounce is =2.16 
cubic in. 

A gallon weighs 8 pounds. 

A dry gallon will hold 10 liquid pints=to 10 pounds of 
water; and a bushel will hold 10 liquid gallons=8o lbs. of water. 

A bushel of wheat will weigh 64 lbs . 

A cubic inch contains 200 dry grains. 

A wet grain is— 4 units; a dry grain is=5 units. 

TABLE AVOIRDUPOIS. 

Units. 
27648 

1728 
2l6 

4 

But we have in use amongst us another system of weights 
and measures in which the volume is constant and the weights 
vary . 

This is the Troy and Apothecary system: 

TROY WEIGHT. 
Po. Ou. Dr. Scrup. Grs. Cub. in. Units. 

I 12 96 288 5760 28.8 28800 

I 8 24 480 2.4 2400 

1 3 60 .3 300 

1 20 .1 100 

1 .005 5 

APOTHECARIES MEASURE. 
Gal. Pts. Fl. Ou. Fl. Dr. Min. Cub. in. Units. 

I 8 128 1280 57600 230.4 230400 

I 16 160 7200 28.8 28800 

I 10 450 1.8 1800 

I 45 .18 180 

I — — .004 4 

Now what is the measure of volume which is common tO' 
these two tables ? 

From the small number of grains in the Troy pound it is 
evidently a dry pound. 



THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 27 

5760 x .005=28.8 cubic inches. 

The Apothecaries pound is propt-rly 7200 grains. 

7200 x .004=28.8 

So 28.8 cubic in. is the size of the common measure. 

But that is the Apothecaries pint, and is so found in the 
tables to-day. It is also a pound; so "a pint's a pound the world 
around." 

That is it will hold a pound Troy of wheat, and an Apothe- 
caries pound of water. 

There are twelve ounces in a Troy pound, 28.8 divided by 
12=2.4 cubic inches, which is the size of the Troy ounce. 

There are sixteen ounces in the Apotheca^ pound — 28.8 
divided by 16=1.8 cubic inches; and that is the size of the 
Apothecary ounce to-day. 

How many grains are in the Troy ounce ? 

In two cubic inches there are 400 dry grains; in four tenths 
of an inch there are 80 grs. So there are 480 grs. in the Troy 
ounce. 

How many grains are in the Apothecaries ounce ? 

In one cubic inch there are 250 wet grains; in eight tenths 
of an inch there are 200 grs. So there are 450 grs. in the Apoth- 
ecaries ounce; not 455^ grains as set down in the modern tables. 

Like the modern Avoirdupois ounce, that is five and a half 
grains to much, and for the same reason, the grain has become 
too small. These results go to show that the grains of .004 and 
.005 cubic inches are correct. 

The cubic foot will contain 720 Troy ounces, and 960 Apoth- 
ecary ounces. 

It will contain 60 lbs. Troy of wheat, or 60 Apothecary 
pounds of water, and 60 pints and 30 quarts. 

The Avoirdupois or cubic system, has come down from 
unknown antiquity. But where does the Troy system come from? 

Maybe we can find out. 

Near the centre of the Great Pyramid of Egypt is a large,, 
elegant room, lined with polished red stone. 

In that chamber is a monolithic stone box made of the same 
polished red granite. 



28 THE YARD OR THE METRE, WHICH WILL YE CHOOSE. 

Many persons have measured that stone box with a view of 
ascertaining its cubical contents, but no two of them have agreed 
exactly in their measurements. They vary from the 71 1 18 cubic 
in. of Prof. Greaves to the 72000 cubic in. of Sir Flinders Petrie. 

Now how would a skilled mechanic proceed if requested to 
measure the inside of a rectangular box. 

Would he measure around the top and down the side ? or 
would he measure around the top and around the bottom and 
down both sides, and average them ? 

He would do nothing of the kind. 

He would measure halfway down the middle of the length, 
half way down the middle of the breadth, and down the middle of 
the chest at the centre, and then he would tell you at once the 
contents of the box. 

Knowing this, long before Sir Flinders Petrie went to Egypt, 
I had arrived at the same conclusion that he did, and had pub- 
lished it from Prof. Piazzi Snath's middle measures. 

in. in. in. 

Here they are — 78.08 x 34.41 x 26.80=72004 cubic inches. 

Now any mathematician knows that if that box was intended 
for a standard of volume, that those four inches are a slight plus. 
And as Prof. Smyth went out to prove that the box was so in- 
tended, and as Sir Flinders Petrie went out to prove that it 
wasn't, when two such men substantially agree we must con- 
clude that they are about right. 

Now what is the result of that measure of 72000 cubic in. ? 
Why, it is that the Apothecaries pint is contained just 2500 
times in that stone box. That is, that as that pint will hold one 
pound Troy of wheat and one pound Apothecary of water, that 
that stone box will hold 2500 pounds Troy of wheat, and 2500 
pounds Apothecary of water. 

So there's where you get the Troy weight from, and from 
whoever put it there. I might add that the box will contain 
40000 Apothecary ounces and 30000 Troy ounces and 72000000 
units of volume. 

You have here two very perfect systems of weight and 
measure, the Avoirdupois and the Troy, one with a constant 
weight and different measures, and the other of one measure and 



THE YARD OR THE METRE, WHICH WILE YE CHOOSE. 29 

varying weights ; which will 3 r e choose ? This difficulty con- 
fronts all systems of weight and measure. The litre is one meas- 
ure and different weights, but it is confronted with this same 
problem of one weight and various measures. 

We get around this difficulty, if it is one, by adopting them 
both; and as each has some advantages of its own, and as each is 
applied practically to different purposes, they mutually supple- 
ment each other. 

As the unit of volume is the same in both, and the grains 
the same and the inch the same, and as 5 pounds Avoirdupois 
are equal to 6 pounds Troy, they can readily be converted one 
into the other. 

I have thus shown that our systems of weight and measure 
are substantially perfect, and that the Metric system is exceed- 
ingly limited; that its decimalization is imperfect and that to us 
it is useless. I so submit the case. 

The yard or the metre, which will ye choose ? 




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